Go out and buy 10,000 100-watt
light bulbs and arrange them in 100 rows of 100 bulbs
each. Then plug them in and turn them on. The resulting
megawatt of radiated power is close to what the 305-meter
Arecibo
Telescope transmits in an asteroid radar experiment.
The 70-meter Goldstone
Antenna transmits half of that, but it can look at
the entire sky while Arecibo can point only within 20
degrees from zenith. These two complementary instruments,
which have obtained radar
echoes from dozens of NEAs, are remarkably sensitive:
the power that they can detect is less than what is
expended by an ant that climbs up the wall of your room
in a time longer than the age of the universe.

When we do an asteroid radar experiment,
we measure the time it takes the echo to return with a
resolution as fine as a tenth of a microsecond, which
tells the asteroid's distance with a resolution as fine
as a decameter. We also measure the echo's Doppler
frequency shift, which tells us the asteroid's
line-of-sight speed with a resolution that can be as
small as the speed of the tip of a clock's minute hand.
The fractional precision of radar
astrometry is typically between 10-6 and
10-8, making it very powerful in refining
asteroid orbits. The distribution of an asteroid's
echo power in time delay and Doppler frequency forms a
two-dimensional image whose geometry can be visualized as
follows. The radar observation cuts the asteroid into
rectangular cells using two sets of parallel planes, one
set parallel to the plane of the sky and one set parallel
to both the line of sight and the asteroid's rotation
pole. Within any given cell, there can be surface regions
in both the northern and southern "hemispheres"
that give echo, so the image contains ambiguities that do
not afflict normal optical pictures.

Fortunately, if a sequence of radar
images can be obtained with the asteroid in a lot of
orientations, then one can solve for both the shape and the spin
state. Scott Hudson
first figured out how to do this, and the result has been
publication of computer models for the shapes of several
asteroids, most of which also are available as replicas
tthat you can hold in your hand. Radar observations have revealed a variety
of exotic NEAs, including a two-kilometer-wide piece of metal ( 6178
(1986DA)), a world shaped like a paramecium (Geographos),
asteroids in non-principal-axis spin states (Toutatis
and 1999
JM8), contact-binary shapes (e.g.,Castalia)
and binary systems (e.g., 1999 KW4),
and one tiny, rapidly rotating, spheroidal, carbonaceous monolith
that is a prime candidate for people to visit and eventually
assimilate (1998 KY26)
.